Two new integrable couplings of the soliton hierarchies with self-consistent sources

doi:10.1088/1674-1056/19/10/100303

Abstract A kind of integrable coupling of soliton equations hierarchy with self-consistent sources associated with $\widetilde{sl}$(4) has been presented (Yu F J and Li L 2009 Appl. Math. Comput. 207 171; Yu F J 2008 Phys. Lett. A 372 6613). Based on this method, we construct two integrable couplings of the soliton hierarchy with self-consistent sources by using the loop algebra $\widetilde{sl}$(4). In this paper, we also point out that there are some errors in these references and we have corrected these errors and set up new formula. The method can be generalized to other soliton hierarchy with self-consistent sources.

Keywords: TC hierarchy generalized Burgers hierarchy self-consistent sources integrable couplings loop algebra

Received: 26 October 2009
Revised: 29 March 2010
Accepted manuscript online:

PACS:	02.10.Ud	(Linear algebra)
	02.30.Ik	(Integrable systems)
	05.45.Yv	(Solitons)

Fund: Project supported by the Natural Science Foundation of Shanghai (Grant No. 09ZR1410800), the Science Foundation of Key Laboratory of Mathematics Mechanization (Grant No. KLMM0806), the Shanghai Leading Academic Discipline Project (Grant No. J50101), the Key Disciplines of Shanghai Municipality (Grant No. S30104), and the National Natural Science Foundation of China (Grant Nos. 61072147 and 11071159).

Cite this article:

Xia Tie-Cheng(夏铁成) Two new integrable couplings of the soliton hierarchies with self-consistent sources 2010 Chin. Phys. B 19 100303

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